Range Of Richardson Numbers Research Articles

Experimental and numerical investigations on a solar tracking concentrated photovoltaic–thermal system with a novel non-dimensional lattice Boltzmann method

A small scale solar tracking concentrated photovoltaic–thermal (CPV–T) system was investigated to enhance the energy efficiency of photovoltaic systems. The experimental measurement was firstly done to obtain the environmental parameters and on site efficiencies of the system. A novel Non-Dimensional Lattice Boltzmann Method (NDLBM) was then developed to simulate the transient fluid flow and heat transfer of the CPV–T receiver. This NDLBM establishes a whole set of dimensionless form of lattice Boltzmann equations and boundary conditions with dimensionless governing parameters in both macroscopic and mesoscopic length scales. The relaxation time is expressed in form of the mesoscopic Reynolds number instead of the viscosity, making the relationship between the mesh size and simulation range clearer. The present physics-based dimensionless inlet/outlet flow and heat flux boundary conditions make it possible to simulate the present high solar irradiance, large temperature difference, and high velocity mixed convection heat transfer problem. The effects of the flow rate, inlet flow temperature and distributions of the inlet/outlet on the heat transfer are obtained with NDLBM simulations over a wide range of Reynolds number, Rayleigh number, and Richardson number. The results provide a full understanding of the mechanics of the efficiency enhancement of the CPV–T system due to water cooling.

Effects of an adiabatic inclined fin on the mixed convection heat transfer in a square cavity

In this study, a square cavity with two ventilation ports in the presence of an adiabatic fin placed on the bottom wall of the cavity is numerically analysed for the mixed convection case for a range of Richardson numbers (Ri = 0.1,1, 10, 30) and at Reynolds number of 300. The top and bottom walls of the cavity are kept at constant temperature while the verticals walls are assumed to be adiabatic. The effect of the fin height, inclination angle and Richardson number on the fluid flow and heat characteristics is numerically analysed. The results are presented in terms of streamlines, isotherm plots and averaged Nusselt number plots. It is observed that length and inclination angle of the fin significantly alter the streamlines and isotherms and hence the thermal performance of the system. For the best performance at different fin lengths, optimum inclination angle changes.

Effects of an adiabatic fin on the mixed convection heat transfer in a square cavity with two ventilation ports

In this study, a square cavity with two ventilation ports in the presence of an adi-abatic fin of different lengths placed on the walls of the cavity is numerically analyzed for the mixed convection case for a range of Richardson numbers (Ri=0.1,1, 10, 100) and at Reynolds number of 300. The effect of the fin height, placement of the fin on each of the four walls of the cavity and Richardson number on the heat transfer and fluid flow characteristics is numerically analyzed. The results are presented in terms of streamlines, isotherm plots and averaged Nusselt number plots. It is observed that for the convection dominated case, fin length and its position on the one of the four walls of the cavity do not alter the thermal performance whereas when the buoyancy effects become important thermal performance increases for high fin length.

Direct Numerical Simulations of a Smoke Cloud–Top Mixing Layer as a Model for Stratocumuli

Abstract A radiatively driven cloud-top mixing layer is investigated using direct numerical simulations. This configuration mimics the mixing process across the inversion that bounds the stratocumulus-topped boundary layer. The main focus of this paper is on small-scale turbulence. The finest resolution (7.4 cm) is about two orders of magnitude finer than that in cloud large-eddy simulations (LES). A one-dimensional horizontally averaged model is employed for the radiation. The results show that the definition of the inversion point with the mean buoyancy of 〈b〉(zi) = 0 leads to convective turbulent scalings in the cloud bulk consistent with the Deardorff theory. Three mechanisms contribute to the entrainment by cooling the inversion layer: a molecular flux, a turbulent flux, and the direct radiative cooling by the smoke inside the inversion layer. In the simulations the molecular flux is negligible, but the direct cooling reaches values comparable to the turbulent flux as the inversion layer thickens. The results suggest that the direct cooling might be overestimated in less-resolved models like LES, resulting in an excessive entrainment. The scaled turbulent flux is independent of the stratification for the range of Richardson numbers studied here. As suggested by earlier studies, the turbulent entrainment only occurs at the small scales and eddies larger than approximately four optical lengths (60 m in a typical stratocumulus cloud) perform little or no entrainment. Based on those results, a parameterization is proposed that accounts for a large part (50%–100%) of the entrainment velocities measured in the Second Dynamics and Chemistry of the Marine Stratocumulus (DYCOMS II) campaign.

Numerical analysis and identification of mixed convection in pulsating flow in a square cavity with two ventilation ports in the presence of a heating block

In this study, a square cavity with two ventilation ports in the presence of a isothermal heating block placed in the middle of the cavity is numerically analyzed for the mixed convection case in pulsating flow for a range of Richardson numbers (Ri = 1, 10, 100) and at Reynolds number of 300. At the inlet of the ventilation port, pulsating velocity is imposed for Strouhal numbers of 0.1, 0.5, 1, 2.5, 5 and velocity amplitude ratio of 0.3, 0.6 and 0.9. The effect of the pulsation frequency, amplitude and Richardson number on the heat transfer and fluid flow characteristics is numerically analyzed. The results are presented in terms of streamlines, isotherm plots and averaged Nusselt number plots. A neural network-based identification approach is utilized for the low amplitude of pulsating velocity to obtain an input–output model for the heat transfer for a range of pulsating frequencies.

Unsteady mixed convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

A two-dimensional numerical study is carried out to understand the influence of cross buoyancy on the vortex shedding processes behind two equal isothermal square cylinders placed in a tandem arrangement at low Reynolds numbers. The spacing between the cylinders is fixed with five widths of the cylinder dimension. The flow is considered in an unbounded medium, however, fictitious confining boundaries are chosen to make the problem computationally feasible. Numerical calculations are performed by using a finite volume method based on the PISO algorithm in a collocated grid system. The range of Reynolds number is chosen to be 50–150. The flow is unsteady laminar and two-dimensional in this Reynolds number range. The mixed convection effect is studied for Richardson number range of 0–2 and the Prandtl number is chosen constant as 0.71. The effect of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as overall drag and lift coefficients, local and surface average Nusselt numbers and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.

Buoyancy driven flow and heat transfer of nanofluids past a square cylinder in vertically upward flow

The present work simulates the buoyancy driven mixed convective flow and heat transfer characteristics of water-based nanofluid past a square cylinder in vertically upward flow using a SUPG (Streamline Upwind Petrov–Galerkin) based finite element method. Nano sized copper (Cu) and alumina (Al2O3) particles suspended in water are used with Prandtl number (Pr)=6.9. The range of nanoparticle volume fractions (ϕ) considered is 0⩽ϕ⩽20%. Computations are carried out at a representative Reynolds number (Re) of 100. Effect of aiding and opposing buoyancy is brought about by considering the Richardson number (Ri) range −0.5⩽Ri⩽0.5. Al2O3–water and Cu–water nanofluids show suppression of vortex shedding at Ri⩾0.15. Vortex shedding process is initiated and a completely new phenomenon is discovered when the nanofluid solid volume fraction,ϕ, is increased. For Al2O3–water nanofluids, at Ri=0.15, completely periodic vortex shedding is found for ϕ⩾10%. For Cu–water nanofluid, shedding is observed for both Ri=0.15 and Ri=0.5. At Ri=0.15 shedding is found at ϕ⩾5%, whereas at Ri=0.5 it is at ϕ⩾15%. A new expression for convective instability of nanofluids is derived to calculate critical nanofluid solid volume fraction. The local Nusselt number increases with increasing ϕ. At a fixed ϕ, the time averaged local Nusselt number is higher for Cu–water nanofluids, as compared to Al2O3–water nanofluids. The average Nusselt number (Nuavg) increases with the concentration of ϕ. Cu–water based nanofluids show higher magnitudes of Nuavg compared to Al2O3–water nanofluids.

Numerical Analysis and POD based Interpolation of Mixed Convection Heat Transfer in Horizontal Channel with Cavity Heated from Below

In this study, a channel with a cavity heated from below is numerically investigated for the mixed convection case for a range of Richardson numbers (Ri=0.1, 1, 5, 10, 15 and 20) and Reynolds numbers (Re=400, 500, 600, 700 and 800) in the laminar flow regime. The results are presented in terms of streamlines, isotherm plots, local Nusselt number distribution along the bottom wall of the cavity and averaged Nusselt number plots. A POD-based interpolation method is also employed to predict the flow field and heat transfer characteristic for the mixed convection case at Re=400 for a range of Richardson numbers. Excellent agreement between the field variables is obtained for the considered range (Ri=0.1, 1, 2, 5, 10, 15 and 20) and targeted (Ri=3, 7 and 12) Richardson numbers. Nusselt number variation with respect to Richardson number is also captured well with this approach of POD-based interpolation compared to the CFD calculations.

Mixed Convection Heat Transfer from Tandem Square Cylinders for Various Gap to Size Ratios

This article presents a two-dimensional numerical study on the fluid flow and mixed convection heat transfer around two equal isothermal square cylinders placed in a tandem arrangement and subjected to the cross flow of a Newtonian fluid at moderate Reynolds numbers. The spacing between the cylinders is varied by changing the gap to cylinder size ratio as S/d = 1, 2, 3, 4, 5, 7, and 10. The Reynolds number is considered in the range 50 ≤ Re ≤ 150. The mixed convection effect is studied for Richardson number range of 0–2, and the Prandtl number is chosen constant as 0.71. The flow is considered in an unbounded medium; however, fictitious confining boundaries are chosen to make the problem computationally feasible. Numerical calculations are performed by using a PISO algorithm-based finite volume solver in a collocated grid system. The effect of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as overall drag and lift coefficients, local and surface average Nusselt numbers, and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers and spacing ratios. The notable contribution is the quantification of the critical spacing ratio which is observed to decrease with increasing thermal buoyancy effect for a specific Reynolds number.

The effect of canyon aspect ratio on flushing of dense pollutants from an isolated street canyon

This study presents an experimental investigation of the effect of canyon aspect ratio on the dense pollutant removal from a street canyon by a turbulent overflow. Four series of experiments for different aspect ratios (η=0.45, 0.75, 1, 2) were conducted for a range of Richardson numbers. The qualitative and quantitative results are discussed and compared. Increasing the Richardson number and decreasing the canyon aspect ratio resulted in an increasingly strong stratification within the canyon and longer trapping times for the pollutant. The aspect ratio strongly affects the initial flushing mechanics and subsequent flow regime within the canyon. Narrower street canyons limit the width of large-scale vortices in the canyon and hence reduce vertical mixing. Based on the initial Richardson number, for all geometric configurations, three different flow regimes were observed in the canyon. The Richardson number at which there is a transition between these regimes is a function of the canyon geometry.

Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Square Cylinder in Vertically Upward Flow

The present work demonstrates entropy generation due to laminar mixed convection of water-based nanofluid past a square cylinder in vertically upward flow. Streamline upwind Petrov–Galerkin (SUPG) based finite element method is used for numerical simulation. Nanosized copper (Cu) and alumina (Al2O3) particles suspended in water are used with Prandtl number (Pr) = 6.2. The range of nanoparticle volume fractions considered is 0–20%. Computations are carried out at a representative Reynolds number (Re) of 100 with Richardson number (Ri) range −0.5 < Ri < 0.5, both values inclusive. For both the nanofluids (Al2O3–water and Cu–water nanofluids), total entropy generation decreases with increasing nanoparticle volume fractions. It is found that for the present case of mixed convection flows with nanofluids, thermal irreversibility is much higher than that of frictional irreversibility. The Bejan number decreases with increasing nanoparticle volume fractions.

Shear-driven flushing of dense fluid from a canyon

The mechanics of shear-driven flushing of a dense fluid from a canyon is considered through a series of laboratory experiments. Experiments are presented for a range of canyon aspect ratios and flow Richardson numbers. The dynamics of the mixing is discussed qualitatively and four separate flow regimes are identified. The flow regime observed is shown to be dependent on both the canyon aspect ratio and the flow Richardson number. For taller, narrower canyons and higher Richardson numbers a two-layer stratification is observed throughout the flushing process. For wider canyons and intermediate Richardson numbers the canyon remains stably stratified but no distinct layers are observed. For low Richardson numbers and wide canyons, the canyon is relatively well mixed during the whole flushing process. A regime diagram showing the flow observed in Richardson number–aspect ratio space is presented.

Numerical Simulation of Mixed Convection Flows in a Square Double Lid-Driven Cavity Partially Heated Using Nanofluid

A numerical study has been done through an Al2O3–water in a double lid-driven square cavity with various inclination angles and discrete heat sources. The top and right moving walls are at low temperature. Half of the left and bottom walls are insulated and the temperatures of the other half are kept at high. A large number of simulations for a wide range of Richardson number of 0.1 to 10, Reynolds number from 1 to 100, inclination angle of cavity from -90 o to 90 o and solid volume fraction between 0 and 0.06 are performed. The results are presented in the form of streamline, isotherm and Nusselt number plots. The influence of solid volume fraction of nanofluids and angle of inclination on hydrodynamic and thermal characteristics have been analyzed and discussed. As a result, it was found that the heat transfer increases with increase in solid volume fraction for a constant Reynolds number, heat transfer also increases with increase in Richardson and Reynolds for a particular volume fraction.

Mixed convection in a lid driven square cavity with an isothermally heated square blockage inside

Laminar mixed convection characteristics in a square cavity with an isothermally heated square blockage inside have been investigated numerically using the finite volume method of the ANSYS FLUENT commercial CFD code. Various different blockage sizes and concentric and eccentric placement of the blockage inside the cavity have been considered. The blockage is maintained at a hot temperature, Th, and four surfaces of the cavity (including the lid) are maintained at a cold temperature, Tc, under all circumstances. The physical problem is represented mathematically by sets of governing conservation equations of mass, momentum, and energy. The geometrical and flow parameters for the problem are the blockage ratio (B), the blockage placement eccentricities (ɛx and ɛy), the Reynolds number (Re), the Grashof number (Gr), and the Richardson number (Ri). The flow and heat transfer behavior in the cavity for a range of Richardson number (0.01–100) at a fixed Reynolds number (100) and Prandtl number (0.71) is examined comprehensively. The variations of the average and local Nusselt number at the blockage surface at various Richardson numbers for different blockage sizes and placement eccentricities are presented. From the analysis of the mixed convection process, it is found that for any size of the blockage placed anywhere in the cavity, the average Nusselt number does not change significantly with increasing Richardson number until it approaches the value of the order of 1 beyond which the average Nusselt number increases rapidly with the Richardson number. For the central placement of the blockage at any fixed Richardson number, the average Nusselt number decreases with increasing blockage ratio and reaches a minimum at around a blockage ratio of slightly larger than 1/2. For further increase of the blockage ratio, the average Nusselt number increases again and becomes independent of the Richardson number. The most preferable heat transfer (based on the average Nusselt number) is obtained when the blockage is placed around the top left and the bottom right corners of the cavity.

Conduction-combined forced and natural convection in a lid-driven parallelogram-shaped enclosure divided by a solid partition

Conduction-combined forced and natural convection heat transfer flow of air in a differentially heated lid-driven parallelogram-shaped enclosure divided by a solid partition has been formulated and solved numerically using the finite-volume method with the SIMPLE algorithm. For the two-dimensional problem, numerical solutions are obtained for a wide range of Richardson numbers (0.1 ≤Ri ≤ 10), inclination angles of enclosure from the vertical direction (-60° ≤Φ≤ 60°), and thermal conductivity ratios (0.001 ≤K ≤ 10). The results indicate that all of the studied parameters and direction of moving lid have significant effects on Nusselt number and the average skin friction coefficient.

INTERACTION EFFECTS OF HYDRODYNAMICALLY FULLY DEVELOPED PRIMARY FLOW AND SECONDARY FLOW IN THE THERMAL ENTRANCE REGION OF ANNULAR DUCT

Experiments have been conducted to study the local and average heat transfer by mixedconvection for hydrodynamically fully developed, thermally developing and fully developedlaminar upward air flow in an inclined annulus with adiabatic inner cast iron tube and uniformheated outer aluminum tube with an aspect ratio ( Ω = 0.72) and (L/Dh≈40) for both calming andtest sections). A wide range of Reynolds number from 859 to 2024 has been covered, and heatflux has been varied from 159 W/m2 to 812 W/m2 (these values of heat flux and Reynoldsnumber gave Richardson number range from 0.03 to 0.٣٨), with angles of annulus inclinationφ =0o (horizontal position), φ =60o (inclined position), and φ =90o (vertical position). The hydrodynamically fully developed condition has been achieved by using aluminum annulus(calming section) has the same dimensions as test section and has connected with it by Teflonpiece. The average Nusselt numbers have been correlated with the product of (Richardsonnumber and Reynolds number) and compared with available literature and showed satisfactoryagreement. The temperature and local Nusselt number profiles results have revealed that thesecondary flows created by natural convection have a significant effect on the heat transferprocess.

Experimental investigation of flow assisted mixed convection in high porosity foams in vertical channels

This paper reports the results of an experimental study on flow assisted mixed convection in a vertical channel containing aluminium metal foams having different number of pores per inch, with high porosity in the range of 0.9 to 0.95. With a view to delineate the flow regimes, experiments are conducted for a wide range of Richardson numbers 0.005 ⩽ Ri ⩽ 1032. Based on a parametric study with a large number of experimental data, a correlation for the wall Nusselt number in the presence of the porous medium as a function of Richardson number, Reynolds number, and the porosity is developed. The novelty of the present work is the use of a wide range of Richardson and Reynolds numbers covering the forced convection dominant and mixed convection regimes. In order to quantify the enhancement of the heat transfer rate in the presence of porous medium, correlations for (i) Nusselt number for a channel without foam, under mixed convection and (ii) ratio of heat transfer rate with and without porous medium have also been developed. The enhancement ratio is always more than one, which clearly indicates that metal foams invariably enhance heat transfer. However, there is a penalty in terms of increased pressure drop.

Numerical modeling of Kelvin–Helmholtz instability using smoothed particle hydrodynamics

AbstractThis paper presents a Smoothed Particle Hydrodynamics (SPH) solution for the Kelvin–Helmholtz Instability (KHI) problem of an incompressible two‐phase immiscible fluid in a stratified inviscid shear flow with interfacial tension. The time‐dependent evolution of the two‐fluid interface over a wide range of Richardson number (Ri) and for three different density ratios is numerically investigated. The simulation results are compared with analytical solutions in the linear regime. Having captured the physics behind KHI, the effects of gravity and surface tension on a two‐dimensional shear layer are examined independently and together. It is shown that the growth rate of the KHI is mainly controlled by the value of the Ri number, not by the nature of the stabilizing forces. It was observed that the SPH method requires a Richardson number lower than unity (i.e. Ri≅0.8) for the onset of KHI, and that the artificial viscosity plays a significant role in obtaining physically correct simulation results that are in agreement with analytical solutions. The numerical algorithm presented in this work can easily handle two‐phase fluid flow with various density ratios. Copyright © 2011 John Wiley & Sons, Ltd.

Characteristics of mixed convection heat transfer in a lid-driven square cavity with various Richardson and Prandtl numbers

In mixed convection flows, a common knowledge is that the heat transfer in a cavity is increased with increasing Grashof or Reynolds number when its respective Reynolds or Grashof number is kept at constant. On the other words, the heat transfer would increase if the flow proceeds toward pure natural convection or forced convection dominated regimes. An unanswered question is that would the heat transfer be increased continuously with simultaneously increasing both Grashof and Reynolds numbers, while keeping the Richardson and Prandtl numbers constant. And to what extent the mixed convection flows would change from laminar to chaos. These questions motivate the present study to systematically investigate the flow and heat transfer in a 2-D square cavity where the flow is induced by a shear force resulting from the motion of the upper lid combined with buoyancy force due to bottom heating. The numerical simulations cover a wide range of Reynolds (10 ≤ Re ≤ 2200), Grashof (100 ≤ Gr ≤ 4.84 × 10 6), Prandtl (0.01 ≤ Pr ≤ 50), and Richardson (0.01 ≤ Ri ≤ 100) numbers. The average Nusselt numbers are reported to illustrate the influence of flow parameter variations on heat transfer, and they are also compared with the reported Nusselt number correlations to validate the applicability of these correlations in laminar flow regimes. Time traces of the total kinetic energy and average Nusselt number are presented to demonstrate the transition of the flows from laminar to chaos.

Density currents at steady regime

This work brings as its main contribution the study of the phenomenon of density currents in non-stratified reservoirs, with flows in steady regimes. Flows are analyzed for a wide range of Reynolds and Richardson numbers in the entrance of the reservoir. Based on this hypothesis, a hybrid numeric model is presented considering the Reynolds Transport's Equation - focusing on the conservation for volume, mass and momentum - with the intention of obtaining three-dimensional components of velocities, reduced acceleration of gravity and geometric characteristics of currents along the reservoir. It is possible to notice in the numeric simulations, mainly, the need of complementation of the model that refers to the inclusion of the entrainment coefficient and the analysis in the unsteady regime.